Dampening bullwhip effect of   order-up-to inventory strategies   via  an optimal  control method

Honglei Xu; Peng Sui; Guanglu Zhou; Louis Caccetta

doi:10.3934/naco.2013.3.655

Article Contents

2013, Volume 3, Issue 4: 655-664. Doi: 10.3934/naco.2013.3.655

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Dampening bullwhip effect of order-up-to inventory strategies via an optimal control method

1.
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074
2.
Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025
3.
Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845

Received: February 28, 2013

Revised: September 30, 2013

Published: September 2013

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Abstract

In this paper, we consider the bullwhip effect problem of an Order-Up-To (OUT) inventory strategy for a supply chain system. We firstly establish a new discrete-time dynamical model which is suitable to describe the OUT inventory strategy. Then, we analyze the bullwhip effect for the dynamical model of the supply chain system. We thus transform the bullwhip effect's dampening problem to a discrete-time optimal control problem. By using the Pontryagin's maximum principle, we compute the corresponding optimal control and obtain the optimal manufacturer productivity of goods. Finally, we carry out numerical simulation experiments to show that the devised optimal control strategy is useful to dampen the bullwhip effect which always happens in the supply chain system.

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Mathematics Subject Classification: Primary: 90B50; Secondary: 65P99.

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